Healing capillary films.
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Accepted version
Author(s)
Type
Journal Article
Abstract
Consider the dynamics of a healing film driven by surface tension, that is, the inward spreading process of a liquid film to fill a hole. The film is modelled using the lubrication (or thin-film) approximation, which results in a fourth-order nonlinear partial differential equation. We obtain a self-similar solution describing the early-time relaxation of an initial step-function condition and a family of self-similar solutions governing the finite-time healing. The similarity exponent of this family of solutions
is not determined purely from scaling arguments; instead, the scaling exponent is a function of the finite thickness of the prewetting film, which we determine numerically. Thus, the solutions that govern the finite-time healing are self-similar solutions of the second kind. Laboratory experiments and time-dependent computations of the partial
differential equation are also performed. We compare the self-similar profiles and exponents, obtained by matching the estimated prewetting film thickness, with both measurements in experiments and time-dependent computations near the healing time, and we observe good agreement in each case.
is not determined purely from scaling arguments; instead, the scaling exponent is a function of the finite thickness of the prewetting film, which we determine numerically. Thus, the solutions that govern the finite-time healing are self-similar solutions of the second kind. Laboratory experiments and time-dependent computations of the partial
differential equation are also performed. We compare the self-similar profiles and exponents, obtained by matching the estimated prewetting film thickness, with both measurements in experiments and time-dependent computations near the healing time, and we observe good agreement in each case.
Date Issued
2018-01-16
Date Acceptance
2017-10-03
Citation
Journal of Fluid Mechanics, 2018, 838, pp.404-434
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Start Page
404
End Page
434
Journal / Book Title
Journal of Fluid Mechanics
Volume
838
Copyright Statement
© 2018 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/K008595/1
EP/L020564/1
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
capillary flows
contact lines
thin films
THIN LIQUID-FILMS
VISCOUS GRAVITY CURRENTS
SELF-SIMILAR SOLUTIONS
MOVING CONTACT LINES
DRIVEN FLOWS
DRY SPOT
STABILITY
DYNAMICS
SURFACES
SINGULARITIES
Publication Status
Published